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Sinusoidal Response

R f. R s. +. V in. V o. -. _. +. +. Sinusoidal Response. Linear Resistive Circuits : Determine v o (t) when (a) v in (t) = 2V and (b) v in (t) = 2sin(2 p.1000. t) V The sinusoidal response of linear resistive circuits can be found by finding the DC response with V DC = V m. -. +.

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Sinusoidal Response

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  1. Rf Rs + Vin Vo - _ + + Sinusoidal Response • Linear Resistive Circuits: Determine vo(t) when (a) vin(t) = 2V and (b) vin(t) = 2sin(2p.1000.t) V The sinusoidal response of linear resistive circuits can be found by finding the DC response with VDC = Vm

  2. - + + Sinusoidal Response • Circuits that contain inductors and/or capacitors: Determine vo(t) when (a) vin(t) = 2V and (b) vin(t) = 2sin(2p.1000.t) V Rf L Rs + Vin Vo _

  3. Im b M q Re a Review of Complex Numbers • Rectangular form: • Complex plane: • Polar form:

  4. Addition/Subtraction of Complex Numbers • Given • z1 + z2 = ? Addition/subtraction of complex numbers is performed in rectangular form Im z1+z2 z2 z1 Re

  5. Multiplication/Division of Complex Numbers • Given • z1 z2 = ? and z1/z2 ? multiplication/division of complex numbers is more straightforward in polar form

  6. Phasor Analysis • Phasor analysis used for steady state response of circuits that have only sinusoidal signals (sin or cos)

  7. Impedance and Admittance • Impedance: Z = (V/I)Admittance: Y = (I/V) Y = 1/Z where V and I are the phasor voltage and current, respectively. • Ohm’s Law in phasor domain: V = Z I or I = YV • Both KVL and KCL apply in Phasor domain

  8. I + Z1 V Z2 I I2 I1 + V Z1 Z2 + + V1 V2 Series and Parallel Impedances • Series impedances: • Parallel impedances: • Series admittance: • Parallel admittance:

  9. j150.796 -j60.797 43.63mF 0.4H 120 Vi 120W vi(t) + + vo (t) Vo + + Circuit Analysis Using Phasors • Determine vo(t) for vi(t) = 120sin(120pt+30) V

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